U.S. National Security Advisor Condoleezza Rice has discussed efforts to end North Korea's nuclear weapons programs during a meeting with the South Korean president in Seoul. Her visit follows a stop in Beijing, where Chinese leaders stressed their concerns about the U.S. relationship with Taiwan.

At the end of her Asian trip, Ms. Rice met with South Korean President Roh Moo-hyun during a six-hour stop in Seoul.

Officials say the two discussed common concerns, including North Korea's nuclear weapons programs, the U.S. troop realignment in South Korea and the planned deployment of South Korean soldiers to Iraq.

South Korean officials quote Ms. Rice as saying Pyongyang "will be surprised to see how much is possible," if it gives up its nuclear ambitions.

Presidential spokesman Kim Jong-min says the meeting reaffirmed the determination of the two allies to resolve the North Korean nuclear issue diplomatically.

During a meeting with South Korean Foreign Minister Ban Ki-moon she thanked Seoul for its efforts to stabilize Iraq by sending troops to the war-torn country.

Ms. Rice flew to Seoul on Friday from Beijing, where, earlier in the day, she met President Hu Jintao. Mr. Hu told Ms. Rice he hoped their talks would help resolve the issue of Taiwan.

"I think [these talks] are helpful for you to get a comprehensive understanding about the great importance that we attach to the development of U.S.-China relations, and also our serious concern over the question of Taiwan," he said.

Chinese officials strongly object to U.S. weapons sales to the democratic, self-governed island, which Beijing considers part of its territory.

A U.S. official traveling with Ms. Rice says she addressed China's concerns by reaffirming that Washington does not support independence for Taiwan.

In greeting President Hu, Ms. Rice conveyed a message from President Bush, saying the United States wants to continue developing ties with China.

"Our relationship is developing in a very positive way and the president wants very much to make certain that we have continuous discussions about our relationship," she said.

Ms. Rice encouraged China to support Washington's demand that North Korea give up its nuclear ambitions.

China has organized three rounds of multilateral talks on the issue and is one of the few countries to have influence on North Korea.

On the first stop of her trip, in Tokyo on Wednesday, the U.S. National Security Advisor told Prime Minister Junichiro Koizumi that the United States considers the North Korean nuclear issue an urgent one. Ms. Rice returns to Washington late Friday.